Modeling the Free-Fall Flight of a Ball

Dropped Ball Movie

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Activity: Modeling the Free-Fall Flight of a Ball.

Objective: To help students understand the physics and mathematics of free-fall motion.

A standard model presented in most first-year mathematics courses is that of the free fall flight of a ball given by

s(t) = -(gt^2)/2

This model appears to be straightforward, however, our first attempt to model the data obtained from the video was not immediately successful. The digital camera we used for the video takes 15 frames per second, that is, a picture is taken every 1/15 of a second or every 0.0667 seconds. Thus, the actual instant the ball is dropped could take place between the frames of the video. When this happens, the data or the model must account for a time shift. As a result, we used the shifted model

s(t) = -g/2 (t - to)^2,

where s is the negative distance fallen measured in feet, g is the acceleration due to gravity (feet per second squared), to is the time shift measured in seconds, and t is time measured in seconds.

Click the buttons to see the fit

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